A charitable organization is holding a lottery to raise money. There are 5000 lo

Question

A charitable organization is holding a lottery to raise money. There are 5000 lottery tickets available. For the contest, the organization will randomly choose 50 of these tickets to win prizes. You personally bought 20 tickets. What is the probability that you win exactly 2 prizes? (Note: similar to the card problems we’ve done so often, this drawing is held without replacement. That is, no one ticket can win twice.)

(If you prefer, you may leave your answer in the form of combinations/factorials, without actually typing the calculation into your calculator. (I would advise this, as most calculators will struggle to do factorials this large.))

Explanation / Answer

This is a case of binomial distribution where probability of win =p =50/5000=0.01

and N=20

We need P(x=2) =20C2*(0.01)2(0.99)18 thus answer is 0.0158

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